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The convergence and stability of full discretization scheme for stochastic age-structured population models

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  • Shi, Chunmei

Abstract

In this paper, a fully discretization scheme based on the implicit Euler method (IM) is considered for stochastic age-structured population models. The preservation of the total population with a suitable numerical boundary condition according to the biological meanings are shown. An explicit formula of the numerical basic reproductive number Rh is proposed by the technique that the numerical process is embedded into an l1(R)-valued integrable stochastic process with infinite stochastic Leslie operators. Furthermore, the convergence and connection between Rh and the stability of numerical solution is analyzed. The preservation and detection of the analytic stability through the numerical solutions are discussed for small stepsize. Finally, some numerical experiments including an infection-age model for modified SARS epidemic illustrate the verification and efficiency of our analysis.

Suggested Citation

  • Shi, Chunmei, 2021. "The convergence and stability of full discretization scheme for stochastic age-structured population models," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308201
    DOI: 10.1016/j.amc.2020.125867
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    References listed on IDEAS

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    1. Pei, Yongzhen & Yang, Hongfu & Zhang, Qimin & Shen, Fangfang, 2018. "Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 524-534.
    2. Tan, Jianguo & Rathinasamy, A. & Pei, Yongzhen, 2015. "Convergence of the split-step θ-method for stochastic age-dependent population equations with Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 305-317.
    3. Tan, Jianguo & Men, Weiwei & Pei, Yongzhen & Guo, Yongfeng, 2017. "Construction of positivity preserving numerical method for stochastic age-dependent population equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 57-64.
    4. Ma, Weijun & Ding, Baocang & Zhang, Qimin, 2015. "The existence and asymptotic behaviour of energy solutions to stochastic age-dependent population equations driven by Levy processes," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 656-665.
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